Concept:

In direct bandgap semiconductors, the conduction band minimum and valence band maximum align at the same crystal momentum (\( k = 0 \)), allowing first-order optical transitions that conserve momentum without requiring lattice phonons.

Formula:

$$\text{Direct Transition: } \Delta k = 0 \implies e^- + h^+ \longleftrightarrow h f \quad (\text{High Transition Probability})$$

$$\text{Indirect Transition: } \Delta k \ne 0 \implies e^- + h^+ + \text{Phonon} \longleftrightarrow h f \quad (\text{Low Transition Probability})$$

Solution:

• Photons carry negligible momentum compared to crystal electrons.



• In direct bandgap materials, electrons can transition vertically between bands without changing momentum, enabling fast, efficient photon absorption and emission.



• In indirect materials (Si, Ge), transitions require an interaction with a phonon to conserve momentum, making optical absorption weaker and light emission very inefficient.

Why other options are incorrect:

• Option A: All semiconductors consist of atoms with nuclei and electrons.
• Option B: Direct semiconductors have finite resistivity determined by doping and mobility.
• Option C: Indirect semiconductors can absorb light, but with lower absorption coefficients near the band edge.